Can someone please help me with some integral homework before I shoot the crap out of my calculus book pretty please?! Equation in the forum

- anonymous

- schrodinger

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- anonymous

\[\int\limits_{}^{}\ln (\sqrt[3]{x})\]
That is x to the 3 root

- anonymous

hi there

- anonymous

hello = )

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## More answers

- jim_thompson5910

it might help to think of the cube root of x as x^(1/3)

- jim_thompson5910

then use the power rule

- anonymous

ok do u want me to solve it or should i tell u how to do it

- anonymous

ok I got as far to as thinking of x^(1/3) lol

- jim_thompson5910

now use the rule that
integral of x^n = (1/(n+1))*x^(n+1)

- anonymous

if u solve it i give u medal and if i do so you give me one

- anonymous

so do u mean put 1/3 in front of the ln of stuff and then put it in front of the entire integral? bc that's what I did and it said it was wrong = (

- jim_thompson5910

there's no ln involved here

- anonymous

u=x^1/3

- anonymous

ok maybe you should write the whole thing out cuz now you're just confusing me, please, thank you

- jim_thompson5910

does this rule look familiar
|dw:1360297226043:dw|

- jim_thompson5910

sry the +C is nearly cut off

- anonymous

no yeah i already know that lol we're in the chapter of integration by parts and there is a ln involved it's in the front of the x^(1/3)

- anonymous

not to interrupt, but i think the starting point here is
\[\frac{1}{3}\int \ln(x)dx\] which you do either by parts or by memory

- jim_thompson5910

oh my bad, i didn't see the ln at the very beginning
just thought it was cube root of x

- anonymous

its ok

- anonymous

since \(\ln(x)\) is a very common function, it might be benificial just to memorize
\[\int \ln(x)dx=x\ln(x)-x\] you can check by differentiation

- anonymous

yes that's what i did. oh damn nvm hahaha i think i get it I keep getting it confused that the derivative of ln is 1/x and we don't know the integral of ln yet so we have to do integration by parts lol

- anonymous

your answer is therefore
\[\frac{1}{3}\left(x\ln(x)-x \right)\]

- anonymous

you can use taylor series to integrate this easily

- anonymous

but with z=x+1

- anonymous

you guys were a great help! ty! = )

- anonymous

i would memorize it
just like remembering that
\[\frac{d}{dx}\sqrt{x}=\frac{1}{2\sqrt{x}}\]so while your fellow classmates are integrating by parts, you just write down the answer

- anonymous

i won't recommend that method

- anonymous

what about\[\int\limits \ln e^{^{x ^{2}}}dx\]

- anonymous

or

- anonymous

\[\int\limits \ln(x^x)dx\]

- anonymous

or

- anonymous

\[\int\limits \ln(x^2+2x+1)dx\]

- anonymous

so these are 3 examples that can't be used by just memorizing the specific case

- anonymous

so basically use integration by parts like ur class mates

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